Sound propagation in the presence of a resonant surface

The interactions between acoustic waves and an array of resonators are studied. The resonators are arranged periodically on an impedance surface so that the scale separation between sound wavelength and the array period is achieved. An asymptotic multi-scale model which accounts for viscous and thermal losses in the resonators is developed and is used to derive an effective surface admittance. It is shown that the boundary conditions at the surface are substantially modified around the resonance frequency. The pressure field on the surface is nearly canceled leading to a phase shift between the reflected and the incident waves. The array can also behave as an absorbing layer. The predictions of the homogenized model are compared with multiple scattering theory (MST) applied to a finite size array and the limitations of the former are identified. The influence of the surface roughness and local scattering on the reflected wave is discussed.